Solve for $x$ : $ 7|x - 3| + 10 = -1|x - 3| + 8 $
Solution: Add $ {1|x - 3|} $ to both sides: $ \begin{eqnarray} 7|x - 3| + 10 &=& -1|x - 3| + 8 \\ \\ { + 1|x - 3|} && { + 1|x - 3|} \\ \\ 8|x - 3| + 10 &=& 8 \end{eqnarray} $ Subtract ${10}$ from both sides: $ \begin{eqnarray} 8|x - 3| + 10 &=& 8 \\ \\ { - 10} &=& { - 10} \\ \\ 8|x - 3| &=& -2 \end{eqnarray} $ Divide both sides by ${8}$ $ \dfrac{8|x - 3|} {{8}} = \dfrac{-2} {{8}} $ Simplify: $ |x - 3| = -\dfrac{1}{4}$ The absolute value cannot be negative. Therefore, there is no solution.